Warning! This synopsis may contain spoilers

Tevye (Topol), the philosophical village milkman, explains the customs of the Jewish people and their lives in the Russian shtetl of Anatevka in 1905, where life is as precarious as the perch of a fiddler on a roof ("Tradition"). At Tevye's home, everyone is busy preparing for the Sabbath meal. His sharp-tongued wife, Golde (Norma Crane), orders their five daughters, Tzeitel (Rosalind Harris), Hodel (Michele Marsh), Chava (Neva Small), Shprintze (Elaine Edwards), and Bielke (Candy Bonstein), about their tasks.

Yente (Molly Picon), the village matchmaker, arrives with news for Golde. Lazar Wolf (Paul Mann), the wealthy butcher, a widower of Tevye's age, wants to wed Tzeitel, their eldest daughter. Tevye must be persuaded to meet Lazar to arrange the marriage. The two middle daughters, Hodel and Chava, speculate excitedly about what their mother and the matchmaker were talking about, but Tzeitel warns them not be so hasty. They are poor, so their parents will have no choice but to take whatever husband Yente brings ("Matchmaker"). Tzeitel is not eager to have a match found for her, as she is already in love with the tailor, Motel Kamzoil (Leonard Frey), her friend since childhood.

Tevye's horse is lame, and he must pull the milk cart himself. He asks God, who it would hurt "If I Were a Rich Man?" The men of the village confront Tevye, as he is late delivering their milk and cheese. Avram (Alfie Scopp), the bookseller, has news from the outside world about pogroms and expulsions. A student from Kiev, Perchik (Paul Michael Glaser), newly arrived in town, hears their conversation and scolds them for doing nothing more than talk. The men dismiss Perchik as a radical, but Tevye takes a liking to him and invites him home for the Sabbath meal, offering him room and board in exchange for tutoring his two youngest daughters. Golde tells Tevye to meet Lazar Wolf after the Sabbath but does not tell him why, knowing that Tevye does not like Lazar. Tzeitel is afraid that Yente will find her a husband before Motel asks Tevye for her hand. But Motel resists: he is shy and afraid of Tevye's temper, and tradition says that a matchmaker arranges marriages. Motel is also very poor and is saving up to buy a sewing machine before he approaches Tevye, to show that he can support a wife. The family gathers around for the "Sabbath Prayer."

After the Sabbath, Tevye visits Lazar Wolf. Teyve assumes that Lazar wants to buy his milk cow. After the misunderstanding is cleared up, Tevye agrees to let Lazar marry Tzeitel. With a rich butcher, he knows that his daughter will never go hungry. The two go to Mordcha's inn to seal their agreement with a drink. Many of the villagers are there, including a group of non-Jews. All join in the celebration of Lazar's good fortune; even the Russian youths at the inn join in the celebration and show off their dancing skills ("To Life"). Outside the inn, Tevye bumps into the Russian Constable (Louis Zorich), who has jurisdiction over the Jews in the town. The Constable warns him that there is going to be a "demonstration" in the coming weeks (a euphemism for a minor pogrom). The Constable has sympathy for the Jewish community but is powerless to prevent the violence.

The next morning, a hungover Tevye delivers the news to his family that he has agreed that Tzeitel will marry Lazar Wolf. Golde is overjoyed, but Tzeitel is horrified and pleads with Tevye to reconsider. Motel arrives and gathers the courage to tell Tevye that he and Tzeitel gave each other a pledge to marry. Tevye is outraged at this breach of tradition, but Motel argues that even a poor tailor is entitled to some happiness. Tevye is impressed when the once-timid young tailor stands up for himself and, moved by his daughter's earnestness, gives his assent ("Tevye's Monologue"); but he worries about how to break the news to Golde. An overjoyed Motel celebrates with Tzeitel ("Miracle of Miracles").

That night in bed with Golde, Tevye has an inspiration: he tells Golde that he has had a nightmare ("Tevye's Dream"). She offers to interpret his dream, and Tevye "describes" it. Golde's grandmother Tzeitel (for whom their daughter is named) returned from the grave to bless the marriage of her namesake, but to Motel, not to Lazar Wolf. Lazar's formidable wife, Fruma Sarah, also rises from her grave to warn, in graphic terms, of severe retribution if Tzeitel marries Lazar. Tevye's superstitious wife is terrified, and she quickly agrees that Tzeitel must marry Motel, much to Tevye's secret relief.

On the road outside of town, Tevye's middle daughter, the bookish Chava, is teased and intimidated by some Russian youths, but one of them, Fyedka (Ray Lovelock), protects her, dismissing the others. He offers Chava the loan of a book, and a secret relationship begins.

The wedding day of Tzeitel and Motel arrives, and all the Jews join the ceremony ("Sunrise, Sunset") and the celebration ("The Wedding Dance"). Lazar gives a fine gift, but an argument arises with Tevye over the broken agreement. Perchik ends the tiff by breaking another tradition: he crosses the barrier between the men and women to dance with Tevye's daughter Hodel. The celebration ends abruptly when a group of Russians rides into the village to perform the "demonstration." They disrupt the party, damaging the wedding gifts and wounding Perchik, who attempts to fight back, and wreaking more destruction in the village. Ever practical, Tevye advises everyone to clean up the mess.

Months later, Perchik tells Hodel he must return to Kiev to work for the revolution. He proposes marriage, admitting that he loves her, and says that he will send for her. She agrees ("Now I Have Everything"). They tell Tevye that they are engaged, and he is appalled that they are flouting tradition by making their own match, especially as Perchik is leaving. When he forbids the marriage, Perchik and Hodel inform him that they do not seek his permission, only his blessing. After some soul searching, Tevye finally relents; the world is changing, and he must change with it ("Tevye's Rebuttal").

Tevye explains these events to an astonished Golde. "Love," he says, "it's the new style." Tevye asks Golde, "Do You Love Me?" She admits that after 25 years of living and struggling together and raising five daughters, she does. Other events are moving apace. Yente tells Tzeitel that she saw Chava with Fyedka. News spreads quickly in Anatevka ("The Rumor"). Perchik has been arrested and exiled to Siberia, and Hodel is determined to join him there. At the railway station, she explains to her father that her home is with her beloved wherever he may be, yet she will always love her family ("Far from the Home I Love").

Weeks pass, and Chava finally gathers the courage to ask Tevye to allow her marriage to Fyedka. Again Tevye reaches deep into his soul, but marriage outside the Jewish faith is a line that he cannot cross. He forbids Chava ever to speak to Fyedka again. When Golde brings the news that Chava has eloped with Fyedka, Tevye wonders where he went wrong ("Chava Sequence"). Chava returns and tries to reason with him, but he refuses to speak to her and tells the rest of the family to consider her dead. Meanwhile, rumors are spreading of the Russians forcing Jewish villagers to leave their villages. While the villagers are gathered, the Constable arrives to tell everyone that they have three days to pack up and leave the town. In shock, they reminisce about the miserable town, and how hard it will be to leave what has for so long been their home ("Anatevka").

As the Jews leave Anatevka, Chava and Fyedka stop to tell her family that they too are leaving. Her mother and sisters are afraid to talk to her with Tevye present. Although Tevye does not speak directly to Chava, he mutters, "God be with you." As Tevye and his family leave the village for America, the fiddler begins to play. Tevye beckons with a nod, and the fiddler follows them out of the village.